Professor Peter Seiler at ECE Spring 2025 Colloquium

Robust Online Convex Optimization for Disturbance Rejection

This talk will consider robust disturbance rejection in high precision applications. We will start by motivating the work with one relevant problem: the control required for optical communication between satellites. We will then discuss the fundamental performance limits associated with linear time invariant (LTI) control. Linear time varying controllers, e.g. those that rely on online convex optimization, can potentially provide significant performance improvements.  However, the ability to accurately adapt to the disturbance while maintaining closed-loop stability relies on having an accurate model of the plant. In fact, the model uncertainty can cause the closed-loop to become unstable. We provide a sufficient condition for robust stability based on the small gain theorem using the ell-infinity norm. This condition is easily incorporated as an on-line constraint in controllers that rely on online convex optimization.